Bandwidth-maintaining multimode optical fibers

ABSTRACT

The specification describes multimode optical fibers with specific design parameters, i.e., controlled refractive index design ratios and dimensions, which render the optical fibers largely immune to moderately severe bends. The modal structure in the optical fibers is also largely unaffected by bending, thus leaving the optical fiber bandwidth essentially unimpaired. Bend performance results were established by DMD measurements of fibers wound on mandrels vs. measurements of fibers with no severe bends.

RELATED APPLICATION

This application claims the benefit of Provisional Application SerialNumber 61097,639, filed Sep. 17, 2008, which application is incorporatedherein by reference.

FIELD OF THE INVENTION

This invention relates to a family of designs for optical fibers havingrobust optical transmission characteristics. More specifically itrelates to optical fibers designed to control bend loss whilemaintaining the modal structure and bandwidth of the fibers.

BACKGROUND OF THE INVENTION

The tendency of optical fibers to leak optical energy when bent has beenknown since the infancy of the technology. It is well known that lightfollows a straight path but can be guided to some extent by providing apath, even a curved path, of high refractive index material surroundedby material of lower refractive index. However, in practice thatprinciple is limited, and optical fibers often have bends with acurvature that exceeds the ability of the light guide to contain thelight.

Controlling transmission characteristics when bent is an issue in nearlyevery practical optical fiber design. The initial approach, and still acommon approach, is to prevent or minimize physical bends in the opticalfiber. While this can be largely achieved in long hauls by designing arobust cable, or in shorter hauls by installing the optical fibers inmicroducts, in all cases the optical fiber must be terminated at eachend. Thus even under the most favorable conditions, bending, oftensevere bending, is encountered at the optical fiber terminals.

Controlling bend loss can also be addressed by the physical design ofthe optical fiber itself. Some optical fibers are inherently more immuneto bend loss than others. This was recognized early, and most opticalfibers are now specifically designed for low loss. The design featuresthat are typically effective for microbend loss control involve theproperties of the optical fiber cladding, usually the outer cladding.Thus ring features or trench features, or combinations thereof, arecommonly found at the outside of the optical fiber refractive indexprofiles to control bend losses. See for example, U.S. Pat. Nos.4,691,990 and 4,852,968, both incorporated herein by reference.

Performance issues for optical fibers under bend conditions havegenerally been considered to involve generalized optical power loss, dueto leakage of light from the optical fiber at the location of the bend.In most cases, the influence of modal structure changes on bend loss isoverlooked.

In single mode optical fibers general power loss is the primaryconsideration, because all leakage involves light in the fundamentalmode of the optical fiber. However, in multimode optical fiber the modalstructure affects the loss, with higher order modes suffering more lossthan lower order modes. In addition, bends in the optical fiber causemodes to transform and mix. Accordingly, while a signal in a lower ordermode may survive some bending, if it is converted to a higher order modeit will be more susceptible to bending loss.

The combination of higher order and lower order modes in a multimodeoptical fiber determines the bandwidth, and thus the signal carryingcapacity, of the optical fiber. Bending multimode optical fiber mayreduce the signal carrying capacity of the optical system.

The property of differential mode loss in multimode optical fibers canbe more serious than generalized optical loss in single mode opticalfibers. The latter can be addressed using low cost power amplifiers.However, differential mode loss in multimode optical fibers can lead tocomplete loss of signals propagating in higher order modes.

STATEMENT OF THE INVENTION

We have designed multimode optical fibers that largely preserve themodal structure, and thus the bandwidth, of the optical fiber even inthe presence of severe bending.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a diagram of an optical fiber refractive index profile showingdesignations for design parameters used in accordance with anembodiment(s) described below. The figure does not represent anydimensional scale;

FIG. 2 is a schematic diagram of an apparatus for measuring DifferentialMode Delay (DMD), a property used for evaluating the performance of theoptical fibers of the invention;

FIGS. 3 a and 3 b are DMD pulse traces showing the effect of bending ona conventional multimode optical fiber;

FIGS. 4 a and 4 b, are DMD traces, to be compared with FIGS. 3 a and 3b, showing the effect of bending on a multimode optical fiber of theinvention;

FIG. 5 is a plot of loss vs. wavelength comparing two multimode opticalfibers, one a conventional optical fiber and the other designedaccording to the invention.

DETAILED DESCRIPTION

With reference to FIG. 1, dimensional design parameters relevant to thepractice of the invention are shown. The vertical reference line, lined1, represents the center of the multimode optical fiber. The sameproportionate profile, with different absolute values, will characterizethe preforms used to manufacture the optical fibers.

It was discovered that for specific controlled design ratios anddimensions multimode optical fibers can be produced that are essentiallyimmune to moderately severe bends. The modal structure is also largelyunaffected by bending, thus leaving the optical fiber bandwidthessentially unimpaired. Ordinary optical fibers demonstrate significantmodal structure change when bent because the high order modes escapeinto the cladding and mid-order modes mix with into high-order modescausing significant changes in the optical fiber bandwidth. Thesechanges are typically measured as differential mode delay (DMD). DMDtechniques and DMD measurements, as related to the invention, will bedescribed in more detail below.

Typical optical fibers, and those to which this invention pertains, havea multimode graded index core with a maximum refractive index in thecenter of the core and with a decreasing refractive index toward thecore/cladding boundary. The decreasing refractive index generallyfollows a parabolic curve defined by the following equations:

d _(c)(r)=d ₁[1−2Δ(r/a ₁)^(α)]^(1/2)  (1)

Δ=(d ₁ ² −d ₂ ²)/2d ₁ ²  (2)

Parameters in the following description relate to those indicated inFIG. 1. The quantities d₁ and d₂ are the refractive indices of the coreat r=0, and r=a₁, respectively. The quantity a₁ is the maximum coreradius and represents the core to clad boundary. The value α is the coreshape profile parameter and defines the shape of the graded refractiveindex profile. The core is surrounded with cladding of radius denoted bya₂. For conventional multimode fibers, the refractive index ismaintained at a value of d₂ in the radial range between a₁ and a₂.

A specific design feature of this invention is that a portion within thecladding region near the core-cladding boundary (denoted between radialposition a₂ and a₃ in FIG. 1), referred to herein as a “trench”, has arefractive index value of d₃ that is different from d2, with a closelycontrolled width (a₃−a₂) within the cladding region. Additionally, theouter cladding refractive index d₄ may be different from the inner valueas denoted by d₂. This negative refractive index region (trench) havingdepths of index (d₃−d₂, d₃−d₄), width (a₃−a₂), together with itslocation relative to the graded index core (a₂−a₁) contributes topreserving the modal structure of the inventive fiber when the fiber istightly bent (as defined later in this description). Thus a newparameter for optical fiber performance is realized and is designated“bend mode performance” (“BMP”), where BMP is the absolute differencebetween the 0-23 micron DMD in a bent state and in an unbent state. Asdefined by the DMD test procedure known as the TIA-FOTP-220 Standard,both the BMP and DMD parameters are expressed in picoseconds per meter,or ps/m.

In formulating designs meeting the inventive criteria, the properties ofthe trench, in particular the trench width a₃−a₂ and the shoulder widtha₂−a₁ were found to have a large effect on the BMP of optical fibers. Infact, within specific ranges of trench widths and shoulder widths, themode structure of the optical fiber can remain essentially unchangedeven when subjected to extreme bending.

As mentioned previously, relevant changes are typically measured asdifferential mode delay (DMD). DMD is the difference in propagation timebetween light energies traveling along different modes in the core of amultimode optical fiber. Multimode optical fiber supports multiple lightpaths, or modes, that carry light from the transmitter to the receiver.When the energy for a laser pulse is transmitted into the optical fiber,it divides into the different paths. As the energy travels along themultimode optical fiber, DMD will cause the pulse to spread beforereaching the receiver. If pulses spread excessively, they may runtogether. When that occurs, the receiver is not able to discern digitalones from zeros, and the link may fail. This is a problem for 1 Gb/ssystems, and limits existing 10 Gb/s systems, and anticipated 40 and 100Gb/s systems, to only modest distances using conventional multimodefiber. Multimode optical fiber DMD is measured in pico-seconds per meter(ps/m) using an OFS-Fitel developed high-resolution process. Thisprocess transmits very short, high-powered 850 nm pulses at manypositions, separated by very small steps, across the core of the opticalfiber. The received pulses are plotted and the data is used withspecially developed OFS software to represent the DMD.

OFS-Fitel pioneered the use of high-resolution DMD as a quality controlmeasure in 1998 to ensure laser bandwidth of production multimodefibers. High-resolution DMD was adopted by international standardscommittees as the most reliable predictor of laser bandwidth for 10Gb/s, and emerging 40 and 100 Gb/s, multimode optical fiber systems.OFS-Fitel co-authored the DMD test procedure known as TIA/EIA-455-220.That procedure has become an industry standard and is widely used onproduction optical fiber to assure reliable system performance for 1 and10 Gb/s systems. The procedure is also being incorporated in thestandards for 40 and 100 Gb/s systems of the future.

The TIA/EIA-455-220 test procedure is schematically represented in FIG.2. The core 23 of the multimode fiber to be tested is scanned radiallywith a single-mode fiber 22 using 850 nm laser emitting pulses 21. Thecorresponding output pulses at the other end of the fiber core arerecorded integrally by the high speed optical receiver on the basis oftheir locations in relation to the radial position of the single modefiber. This provides precise information on the modal delay differencesbetween the selectively-excited mode groups at the various radialoffsets. The DMD scans are then evaluated on the basis of the multiplescans.

DMD scan data is shown in FIGS. 3 a, 3 b, 4 a, and 4 b.

FIGS. 3 a and 3 b demonstrate how the modal structure in other multimodefiber designs changes when bent tightly compared to the unbentcondition.

FIG. 3 a shows a DMD pulse trace demonstrating the modal structure of amultimode optical fiber (MMF) in an unbent condition as defined by theTIA/EIA-455-220 Standard. Notice the outer mode structure between radialpositions 21 micron (shown at 31) and 24 micron (shown at 32). One cansee that at these positions, multiple pulses begin to appear.

FIG. 3 b is a DMD pulse trace demonstrating the modal structure of thesame MMF shown in FIG. 3 a except bent around a 12.8 mm diameter mandrel(defined here as the tightly bent condition). Here the outer modestructure between radial positions 21 micron (shown at 31′) and 24micron (shown at 32′) has undergone a significant change between theunbent condition of FIG. 3 a and the bent condition. Specifically, thepulses shown between 21 and 24 microns in FIG. 3 b have diminishedsignificantly, thus showing a substantial loss in signal power.

In the comparison of FIGS. 3 a and 3 b, it is evident that the outermode structure and the DMD value computed for the 0-23 radial havechanged dramatically. In addition, the power traveling in the outermodes (at 19 microns and beyond) has dropped significantly, suggestingthat the modal energy has been redistributed and more power is escapinginto cladding modes. This redistribution of modal energy has twoeffects. One is that the fiber loss, when bent substantially, increases,as is well known. However, not observed prior to this invention are theeffects on modal structure relative to the bent state.

In bit error rate (BER) systems testing, it has been shown that themodal bandwidth and additional loss in other MMF designs and in standardfibers, results in significant penalties that cause the link to fail(>10⁻¹² BER) when measured under tight bends. With fibers made by thepresent invention, it has been shown that the penalty in BER systemstesting is greatly minimized compared to tests done with other MMF andstandard fibers, and the link operates with better than 10⁻¹² BER.

FIGS. 4 a and 4 b demonstrate that the modal structure for multimodefiber designs according to this invention does not change when benttightly compared to the unbent condition.

FIG. 4 a shows a DMD pulse trace demonstrating the modal structure ofMMF made in accordance with an embodiment of the invention. The pulsetrace of the MMF is shown in FIG. 4 a in the unbent condition. Noticethe outer mode structure between radial positions 21 micron (shown at41) and 24 micron (shown at 42). Similar to the DMD pulse trace shown inFIG. 3 a, pulses begin to appear in the outer mode structure.

FIG. 4 b shows a corresponding DMD pulse trace demonstrating the modalstructure of the same MMF as shown in FIG. 4 a, except bent around a12.8 mm diameter mandrel (the tightly bent condition). Notice the outermode structure between radial positions 21 micron (shown at 41′) and 24micron (shown at 42′) remains unchanged between the unbent and bentconditions. Thus not only is the power loss of the MMF shown in FIGS. 4a and 4 b minimal in the bent state, but the original modal structureremains essentially unchanged and intact.

Having preserved the modal structure, a comparison of the measured addedpower loss for the MMF fiber (upper curve) vs. standard fiber (lowercurve) is illustrated in FIG. 5. The measurement is of the bend loss ofeach fiber with 2 turns around a 10 mm diameter mandrel.

It should be evident that, due to the preservation of high bandwidth inaddition to low bend loss, the improved multimode optical fibers of theinvention need not be restricted to short jumpers. This optical fiberenables applications in, for example, high transmission links; up to 2km at 1 Gb/s, up to 550m at 10 Gb/s, and estimated up to 100m at 40 Gb/sor 100 Gb/s.

Table 1 provides recommended parameters associated with therefractive-index profile shown in FIG. 1. Within the ranges provided forthese parameters, multimode optical fibers with high bandwidth andultra-low bend loss may be simultaneously achieved.

TABLE 1 Designation Parameter Minimum Maximum Optimum a1 Core radius 750 25 +/− 4  μm (a2−a1)/a1 Ratio 0.1 0.7 0.2 +/− 0.1 (a3−a2)/a1 Ratio0.3 0.6 0.4 +/− 0.1 a4 Clad. radius 30 250 62.5 +/− 20   μm d1-d4 IndexΔ −0.019 0.032 0.0137 +/− 0.01  d2-d4 Index Δ −0.01 0.01    0 +/− 0.005d3-d4 Index Δ −0.05 −0.0025 −0.011 +/− 0.008   d4 Index 1.397 1.511 1.46+/− 0.03 Profile shape Alpha 1.6 2.2 2.08 +/− 0.12

As mentioned earlier, one of these parameters, the trench width(expressed in Table I as normalized to the core radius by the equation(a₃-a₂)/a₁) was found to be especially important in determining the bendmode preservation of optical fibers. For example, selecting the midpointof the range for core radius (28.5 microns) of the ranges in Table I,when the minimum value for the parameter (a₃−a₂)/a₁) is 0.3 thecorresponding trench width is 8.55 microns. Expressed as the area of thetrench in a cross section of the optical fiber the area is 1913microns².

The following specific examples give parameters for optical fibers withdemonstrated excellent BMP. Dimensions are in micrometers; area inmicrometers squared.

Example I

Designation Parameter Value a1 Core radius 26.12 a2 Trench start 28.85a3 Trench end 38.9 a4 Clad radius 62.5 d1 Index 1.472 d2 Index 1.457 d3Index 1.449 d4 Index 1.449 Profile shape Alpha 2.08 T_(W) Trench width10.05 T_(A) Trench area 2139

Example II

Designation Parameter Value a1 Core radius 28.4 a2 Trench start 28.81 a3Trench end 40.71 a4 Clad radius 62.5 d1 Index 1.472 d2 Index 1.457 d3Index 1.449 d4 Index 1.457 Profile shape Alpha 2.08 T_(W) Trench width11.9 T_(A) Trench area 2608

Example III

Designation Parameter Value a1 Core radius 24.4 a2 Trench start 28 a3Trench end 40.72 a4 Clad radius 62.5 d1 Index 1.470 d2 Index 1.457 d3Index 1.449 d4 Index 1.457 Profile shape Alpha 2.08 T_(W) Trench width12.72 T_(A) Trench area 2746

Example IV

Designation Parameter Value a1 Core radius 25 a2 Trench start 25.5 a3Trench end 36.9 a4 Clad radius 62.5 d1 Index 1.472 d2 Index 1.457 d3Index 1.449 d4 Index 1.457 Profile shape Alpha 2.08 T_(W) Trench width11.4 T_(A) Trench area 2235

Example V

Designation Parameter Value a1 Core radius 25 a2 Trench start 29.4 a3Trench end 40.75 a4 Clad radius 62.5 d1 Index 1.472 d2 Index 1.457 d3Index 1.449 d4 Index 1.457 Profile shape Alpha 2.08 T_(W) Trench width11.35 T_(A) Trench area 2501

Example VI

Designation Parameter Value a1 Core radius 25 a2 Trench start 27.7 a3Trench end 39.1 a4 Clad radius 62.5 d1 Index 1.472 d2 Index 1.457 d3Index 1.449 d4 Index 1.457 Profile shape Alpha 2.08 T_(W) Trench width11.4 T_(A) Trench area 2391

Example VII

Designation Parameter Value a1 Core radius 25 a2 Trench start 30 a3Trench end 40 a4 Clad radius 62.5 d1 Index 1.472 d2 Index 1.457 d3 Index1.446 d4 Index 1.457 Profile shape Alpha 2.08 T_(W) Trench width 10T_(A) Trench area 2200

Example VIII

Designation Parameter Value a1 Core radius 23.5 a2 Trench start 28 a3Trench end 38.23 a4 Clad radius 62.5 d1 Index 1.470 d2 Index 1.457 d3Index 1.449 d4 Index 1.457 Profile shape Alpha 2.08 T_(W) Trench width10.23 T_(A) Trench area 2129

The values given in these tables are precise values. However, it will beunderstood by those skilled in the art that minor departures, e.g.+/−2%, will still provide performance results comparable to thoseindicated below.

To demonstrate the effectiveness of these optical fiber designs, the BMPwas measured for each Example above and is given in the following table,Table II. The units are picoseconds per meter.

TABLE II Example Condition MW23 BMP 1 Unbent 0.168 0.009 1 Bent 0.159 2Unbent 0.159 −0.002 2 Bent 0.161 3 Unbent 0.298 0.069 3 Bent 0.229 4Unbent 0.884 0.054 4 Bent 0.83 5 Unbent 0.193 0.026 5 Bent 0.167 6Unbent 0.582 0.188 6 Bent 0.394 7 Unbent 0.123 0.004 7 Bent 0.119 8Unbent 0.291 0.06 8 Bent 0.231Two of these design parameters stand out. One is the core radius. It wasfound that optical fibers exhibiting the best mode preservationperformance had a core radius in the range of 22 to 28 microns, but thata properly designed MMF with a core radius in the range 7-50 micronswill also exhibit modal structure integrity. The properties of thetrench are also considered important parameters in designing a BMP. Thetrench width T_(W) should be at least 2.5 microns, and preferablybetween 10 and 13 microns.

Expressed in terms of trench area, T_(A), a range of 1500 to 3500microns² is recommended, and preferably the range is 2000 to 2900microns².

The discovery of this narrow range, in which optical fibers may bedesigned that show excellent BMP, is highly unexpected. The design goalof producing optical fibers that exhibit this unusual behavior is itselfconsidered to be novel in optical fiber technology. Prior todemonstrating the BMP of the eight examples described above thereexisted no indication in the art that optical fibers with this BMP werepossible. The data provided in Table II suggests a target figure ofmerit for BMP. For most of the examples, the absolute variation in the0-23 um DMD values between bent and unbent conditions is within therange of 0 to 0.069 picoseconds per meter. Based on this measuredperformance data, a target figure of merit is an absolute value lessthan 0.07 picoseconds per meter, and preferably less than 0.02picoseconds per meter.

Expressed in terms of trench area, T_(A), a range of 500 to 3500microns² is recommended, and preferably the range is 2000 to 2900microns².

The core delta n in this work is between 0.0125 and 0.016. The trenchdepth (index depth) appears to be a less vital parameter than the width,i.e., larger variations appear to be useful. A trench depth (indexdifference) that is lower than the inner cladding (d₂) by a value of0.0025 to 0.012 is recommended, with a preferred trench depth beingbetween 0.003 to 0.008 lower than the inner cladding (d₂). Thedifference is measured from the next adjacent inner cladding. Refractiveindex differences expressed in this specification refer to indexdifferences based on the index of silica (1.46).

The optical fibers described above may be fabricated using any of avariety of known optical fiber manufacturing techniques, for example,Outside Vapor Deposition (OVD), Chemical Vapor Deposition (CVD),Modified Chemical Vapor Deposition (MCVD), Vapor Axial Deposition (VAD),Plasma enhanced CVD (PCVD), etc.

Various additional modifications of this invention will occur to thoseskilled in the art. All deviations from the specific teachings of thisspecification that basically rely on the principles and theirequivalents through which the art has been advanced are properlyconsidered within the scope of the invention as described and claimed.

1. A multimode optical fiber comprising a core region with a firstradius a₁ and a profile alpha, an inner cladding extending radially froma₁ to second radius a₂, a trench extending radially from second radiusa₂ to a third radius a₃, and an outer cladding extending to a fourthradius a₄, wherein a maximum refractive index of the core region is d₁,a refractive index of the inner cladding is d₂, a refractive index ofthe trench is d₃, and a refractive index of the outer cladding is d₄,wherein: a₁ is 7-50 microns; alpha is 1.6 to 2.2; (a₂−a₁)/a₁ is 0.1 to0.7; (a₃−a₂)/a₁ is 0.3 to 0.6; a₄ is 30-250 microns; d₁−d₄ is −0.019 to0.032; d₂−d₄ is −0.01 to 0.01; d₃−d₄ is −0.05 to −0.0025; and d₄ is 1.4to 1.511.
 2. The optical fiber of claim 1 wherein: a₁ is 21-29 microns;alpha is 1.96 to 2.2; (a₂−a₁)/a₁ is 0.1 to 0.3; (a₃−a₂)/a₁ is 0.3 to0.5; a₄ is 62.5+/−20 microns; d₁−d₄ is 0.0037 to 0.0237; d₂−d₄ is −0.005to 0.005; d₃−d₄ is −0.019 to −0.003; and d₄ is 1.43 to 1.49.
 3. Amultimode optical fiber that exhibits a change in differential modedelay measured as bend mode performance of less than 0.07 picosecondsper meter from an unbent state to bent state, given a reference state of2 turns around a 10 mm diameter.
 4. The optical fiber of claim 3 with acore having a first radius a₁, a trench extending radially from a secondradius a₂ to a third radius a₃, and an outer cladding, and wherein: a₁:22-29 micrometers; and a₃−a₂: at least 2.5 microns.
 5. The optical fiberof claim 4 wherein a₃−a₂ is in the range 10-13 microns.
 6. The opticalfiber of claim 5 additionally having an inner cladding extendingradially from first radius a₁ to second radius a₂, and wherein(a₃−a₂)/a₁ is in the range 0.1 to 0.7.
 7. The optical fiber of claim 3wherein the optical fiber has a core region and a trench, and the trenchhas an area in the range 500-3500 micrometers².
 8. The optical fiber ofclaim 3 wherein the optical fiber has a core region and a trench, andthe trench has an area in the range 2000-2900 micrometers².
 9. Theoptical fiber of claim 7 wherein the trench has a refractive index thatis at least 0.0025 below an inner cladding of the optical fiber.
 10. Theoptical fiber of claim 7 wherein the trench has a refractive index of1.452 or less.
 11. The optical fiber of claim 1 wherein: a₁ is 26.12microns+/−2%; a₂ is 28.85+/−2%; a₃ is 38.9+/−2%; a₄ is 62.5+/−2%; d₁ is1.472+/−2%; d₂ is 1.457+/−2%; d₃ is 1.449+/−2%; d₄ is 1.457+/−2%; andalpha is 2.08+/−2%.
 12. The optical fiber of claim 3 comprising a coreregion with a first radius a₁ and a profile alpha, an inner claddingextending radially from a₁ to second radius a₂, a trench extendingradially from second radius a₂ to a third radius a₃, and an outercladding extending to a fourth radius a₄, wherein a maximum refractiveindex of the core region is d₁, a refractive index of the inner claddingis d₂, a refractive index of the trench is d₃, and a refractive index ofthe outer cladding is d₄, wherein: a₁ is 28.4 microns+/−2%; a₂ is28.81+/−2%; a₃ is 40.71+/−2%; a₄ is 62.5+/−2%; d₁ is 1.472+/−2%; d₂ is1.457+/−2%; d₃ is 1.449+/−2%; d₄ is 1.457+/−2%; and alpha is 2.08+/−2%.13. The optical fiber of claim 1 wherein: a₁ is 24.4 microns+/−2%; a₂ is28+/−2%; a₃ is 40.72+/−2%; a₄ is 62.5+/−2%; d₁ is 1.470+/−2%; d₂ is1.457+/−2%; d₃ is 1.449+/−2%; d₄ is 1.457+/−2%; and alpha is 2.08+/−2%.14. The optical fiber of claim 3 comprising a core region with a firstradius a₁ and a profile alpha, an inner cladding extending radially froma₁ to second radius a₂, a trench extending radially from second radiusa₂ to a third radius a₃, and an outer cladding extending to a fourthradius a₄, wherein a maximum refractive index of the core region is d₁,a refractive index of the inner cladding is d₂, a refractive index ofthe trench is d₃, and a refractive index of the outer cladding is d₄,wherein: a₁ is 25 microns+/−2%; a₂ is 25.5+/−2%; a₃ is 36.9+/−2%; a₄ is62.5+/−2%; d₁ is 1.472+/−2%; d₂ is 1.457+/−2%; d₃ is 1.449+/−2%; d₄ is1.457+/−2%; and alpha is 2.08+/−2%.
 15. The optical fiber of claim 1wherein: a₁ is 25 microns+/−2%; a₂ is 29.4+/−2%; a₃ is 40.75+/−2%; a₄ is62.5+/−2%; d₁ is 1.472+/−2%; d₂ is 1.457+/−2%; d3 is 1.449+/−2%; d₄ is1.457+/−2%; and alpha is 2.08+/−2%.
 16. The optical fiber of claim 1wherein: a₁ is 25 microns+/−2%; a₂ is 27.7+/−2%; a₃ is 39.1+/−2%; a₄ is62.5+/−2%; d₁ is 1.472+/−2%; d₂ is 1.457+/−2%; d₃ is 1.449+/−2%; d₄ is1.457+/−2%; and alpha is 2.08+/−2%.
 17. The optical fiber of claim 1wherein: a₁ is 25 microns+/−2%; a₂ is 30+/−2%; a₃ is 40+/−2%; a₄ is62.5+/−2%; d₁ is 1.472+/−2%; d₂ is 1.457+/−2%; d₃ is 1.446+/−2%; d₄ is1.457+/−2%; and alpha is 2.08+/−2%.
 18. The optical fiber of claim 1wherein: a₁ is 23.5 microns+/−2%; a₂ is 28+/−2%; a₃ is 38.23+/−2%; a₄ is62.5+/−2%; d₁ is 1.470+/−2%; d₂ is 1.457+/−2%; d₃ is 1.449+/−2%; d₄ is1.457+/−2%; and alpha is 2.08+/−2%.
 19. The optical fiber of claim 3comprising a core region with a first radius a₁ and a profile alpha, aninner cladding extending radially from a₁ to second radius a₂, a trenchextending radially from second radius a₂ to a third radius a₃, and anouter cladding extending to a fourth radius a₄, wherein a maximumrefractive index of the core region is d₁, a refractive index of theinner cladding is d₂, a refractive index of the trench is d₃, and arefractive index of the outer cladding is d₄, wherein: a₁ is 25microns+/−2%; a₂ is 34+/−2%; a₃ is 37.6+/−2%; a₄ is 62.5+/−2%; d₁ is1.472+/−2%; d₂ is 1.457+/−2%; d₃ is 1.451+/−2%;
 20. The optical fiber ofclaim 1 wherein the fiber exhibits a change in differential mode delaymeasured as bend mode performance of less than 0.07 picoseconds permeter from an unbent state to bent state, for a reference bent state of2 turns around a 10 mm diameter.
 21. The optical fiber of claim 1wherein the fiber is made using a method selected from the groupconsisting of CVD, OVD, MCVD, PCVD, VAD, and any combinations thereof.22. The optical fiber of claim 3 wherein the fiber is made using amethod selected from the group consisting of CVD, OVD, MCVD, PCVD, VADand any combinations thereof.